1. Field of the Invention
The embodiments of the invention generally relate to calculating critical area, and, more particularly, to calculating critical area of compound fault mechanisms.
2. Description of the Related Art
Critical area is a metric used to determine the sensitivity of a circuit layout to random defects that occur during the manufacturing process. It is a function of the critical defect size at every point and the defect density function. Specifically,
  CriticalArea  =            ∫      xy        ⁢                  ∫                  CriticalDefectSize          ⁡                      (                          x              ,              y                        )                          ∞            ⁢                        DefectDensity          ⁡                      (            r            )                          ⁢                  ⅆ          r                ⁢                  ⅆ          x                ⁢                  ⅆ          y                    The DefectDensity function is a measure of the probability that a random-defect of a particular size r will occur on the chip. It is design-independent and determined by the manufacturing process. The CriticalDefectSize function is the smallest size of the defect centered at a given point (x, y) that would cause an electrical fault. This function is design-dependent. Critical area can be measured based on the particular way a defect causes an electrical fault in the chip (i.e., based on the type of fault mechanism caused by a defect). Exemplary simple fault mechanisms include opens (i.e., wire breaks), shorts, touches and via blockages.
Compound fault mechanisms occur when faults are dependent on the occurrence of two or more independent or dependent faults. Compound fault mechanisms comprising two or more independent faults include, for example, “opens with contacts”, “opens without contacts”, and “opens and contacts.” “Opens with contacts” is a compound fault mechanism in which defects cause a break in a wire OR a via blockage. “Opens without contacts” is a compound fault mechanism in which defects cause a break in a wire but NOT a via blockage. “Opens and contacts” is a compound fault mechanism in which defects cause a break in a wire AND a via blockage at the same time. In general one can compose these compound fault mechanisms by using AND, OR, and NOT relational operators over the simple fault mechanisms. Compound fault mechanisms dependent on the occurrence of two or more dependent faults include, for example, n-level fault mechanisms such as “double-shorts.” “Double-shorts” is a fault mechanism in which a defect must touch two electrically distinct features on two different design levels in order to cause a failure.
Voronoi-based techniques have been used to compute critical area for the simple defect mechanisms based on the design (e.g., as illustrated in the following U.S. patents incorporated herein by reference: U.S. Pat. No. 6,044,208 issued to Papadopoulou et al. on Mar. 28, 2000; U.S. Pat. No. 6,178,539 issued to Papadopoulou et al. on Jan. 23, 2001; U.S. Pat. No. 6,247,853 issued to Papadopoulou et al. on Jun. 19, 2001; and U.S. Pat. No. 6,317,859 issued to Papadopoulou et al. on Nov. 13, 2001). Voronoi-based techniques have further been used to compute compound fault mechanisms comprising independent fault mechanisms (e.g., as illustrated in U.S. Patent Application Pub. No. 2005/0240839 of Allen et al., also incorporated herein by reference). However, the Voronoi-based techniques for computing compound fault mechanisms comprising independent fault mechanism are quite complex. Additionally, these prior art techniques can not be used to compute critical area based on n-level fault mechanisms, such as double-shorts fault mechanisms, because such fault mechanisms are not generally expressible as a composition of other known simple fault mechanisms using only Boolean relations.
Therefore, there remains a need in the art for an improved Voronoi-based technique for more efficiently calculating and detecting the total critical area of a compound fault mechanism, regardless of whether it is independent or dependent in order to improve yield prediction